Background and Objectives: Klebsiella pneumoniae is a major nosocomial pathogen with a remarkable ability to develop resistance to multiple antibiotics, posing significant treatment challenges. This study aims to evaluate the antimicrobial resistance patterns among multidrug-resistant (MDR) and non-MDR strains of K. pneumoniae isolated over a six-year period (2018–2023) at the Clinical Hospital of Infectious Diseases and Pulmonology “Dr. Victor Babes” in Timisoara, Romania. The objectives include categorizing isolates based on their antibiotic resistance profiles and identifying trends in resistance to key antibiotics to optimize treatment strategies and enhance infection control measures. Materials and Methods: A cross-sectional analysis was conducted on K. pneumoniae isolates obtained from various clinical samples between January 2018 and December 2023. Identification was performed using standard bacteriological procedures, and antimicrobial susceptibility testing was conducted using the Kirby–Bauer disk diffusion method in accordance with EUCAST guidelines. Isolates were classified as susceptible, resistant, MDR, extensively drug-resistant (XDR), or pandrug-resistant (PDR) based on ECDC definitions. Data were analyzed using GraphPad Prism 6, with chi-square tests and Cochran–Armitage trend tests applied where appropriate. Statistical significance was set at p < 0.05. Results: A total of 1,081 K. pneumoniae isolates were identified over the six-year period, increasing from 118 isolates in 2018 to 319 in 2023. The proportion of XDR and PDR strains showed a significant upward trend from 30.5% in 2018 to 57.4% in 2023 (p < 0.001). Specifically, XDR strains increased from 22.9% in 2018 to 39.8% in 2023, while PDR strains rose from 7.6% to 17.6%. Among monomicrobial infections in 2023, XDR and PDR strains accounted for 42.4% and 16.5%, respectively. Resistance to carbapenems also showed a significant increase; for instance, resistance to ertapenem rose from 35.6% in 2018 to 54.2% in 2023 (p < 0.001). Subgroup analysis revealed that isolates from bronchial aspirates had the highest rates of XDR and PDR strains in 2023, at 38.0% and 17.2%, respectively. Additionally, polymicrobial infections where both K. pneumoniae and co-infecting pathogens were XDR/PDR increased from 24.2% in 2018 to 46.6% in 2023 (p < 0.001). Conclusions: The study demonstrates a significant escalation in antimicrobial resistance among K. pneumoniae isolates over the six-year period, particularly in XDR and PDR strains. The rising trend of resistance to critical antibiotics like carbapenems underscores the urgent need for enhanced antimicrobial stewardship and infection control measures. Targeted interventions are essential to curb the spread of these resistant strains and to optimize therapeutic strategies.